A New Scoring Algorithm for Multiple-Choice Tests: Conditional Knowledge Model

This paper uses basic rules of probability to develop a new scoring method. The method accounts for guessing, partial knowledge, and misinformation; it also differentiates between incorrect responses and omits. Aside from multiple-choice tests, the method can be used to score short-answer tests. Test scores and confidence intervals are found using simple formulas. Accounting for omits increases test score in almost all cases. Students who guess on questions that they should have omitted are almost always penalized. A counterintuitive finding of this paper is that tests with two answers per question are better able to differentiate between students than tests with higher number of answers per question. In the course of the paper, two new probability density functions are constructed. Their expected values and variances are given.